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Homework Help: Matrix prodect proof

  1. Sep 27, 2008 #1
    Show that if matrix products AB and BA are both defines, then AB and BA are square matrices:

    Let A = a m*n matrix

    IF AB is defined then B must have n rows (n*?) matrix

    IF BA is defined then B must have m columns making it a n*m matrix

    so BA = (n*m) * (m*n) = (n*n) matrix

    AB = (m*n) * (n*m) = (m*m) matrix

    Show that if A is an m*n matrix and A(BA) is defined, then B is an n*m matrix.

    IF BA is defined and A is m*n matrix then B must be a ?*m matrix

    BA produces a ?*n matrix

    IF A(BA) is defined BA must be a n*n matrix

    AS BA is an n*n matrix B must be a n*m matrix

    Do these work as a proofs, if they even follow any logic in the first place (I'm horrid when it comes to matrices)

    Any input would be greatly appreciated :)
  2. jcsd
  3. Sep 27, 2008 #2


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    Science Advisor

    They look perfectly good to me.
  4. Sep 27, 2008 #3
    love you :)
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